# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_pplus(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X1))))),file('i/f/integerRing/int__ring__thms_c53', ch4s_integerRings_intu_u_ringu_u_thmsu_c53)).
fof(4, axiom,![X8]:![X10]:![X1]:![X2]:s(t_h4s_canonicals_canonicalu_u_sum(X8),happ(s(t_fun(t_h4s_ringNorms_polynom(X8),t_h4s_canonicals_canonicalu_u_sum(X8)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_ringNorms_polynom(X8),h4s_ringnorms_pplus(s(t_h4s_ringNorms_polynom(X8),X2),s(t_h4s_ringNorms_polynom(X8),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X8),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X8),t_h4s_canonicals_canonicalu_u_sum(X8)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X8),t_fun(t_h4s_canonicals_canonicalu_u_sum(X8),t_h4s_canonicals_canonicalu_u_sum(X8))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_canonicals_canonicalu_u_sum(X8),happ(s(t_fun(t_h4s_ringNorms_polynom(X8),t_h4s_canonicals_canonicalu_u_sum(X8)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_ringNorms_polynom(X8),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X8),happ(s(t_fun(t_h4s_ringNorms_polynom(X8),t_h4s_canonicals_canonicalu_u_sum(X8)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_ringNorms_polynom(X8),X1))))),file('i/f/integerRing/int__ring__thms_c53', ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c2)).
fof(5, axiom,s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize)=s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c53', ah4s_integerRings_intu_u_polynomu_u_normalizeu_u_def)).
fof(6, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c53', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def)).
# SZS output end CNFRefutation
